What are the numbers a and b ?
I. a and b are relatively prime.
II. L.C.M of a, b is 2550
TS ICET 2015 Question Paper
A question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions.
What is the rate of simple interest on a loan of ₹ 20,000 ?
I. ₹ 23,000 is to be paid at the end of the first year.
II. There is a penal interest of 10% if the loan is not paid at the end of the first year.
Suppose f(x) is a polynomial. Is x - 1 a factor of $$f(x^2 + 7)$$?
I. $$(x - 7) \mid f(x)$$
II. $$(x - 11) \mid f(x - 3)$$
What is the value of xy?
I. $$x^2 = 9$$
II. y = 0
Are the triangles $$\triangle ABE$$ and $$\triangle CDE$$ given below congruent ?
I. $$AB \parallel CD$$
II. $$\angle AEB = \angle CED$$
If $$0 \in \left\{x, y\right\}$$, then what is the value of x + y ?
I. $$x \neq y$$
II. $$x^8 + y = y^8 + x$$
Is $$525 \times k$$ a perfect square?
I. $$21 \mid k$$
II. k = 21
If n(A) denotes the number of elements in the set A, then what is $$n(A \cup B)$$ ?
I. n(A) = 35
II. n(B) = 28
What is the value of the integer $$n \geq 0$$ ?
I. $$25^n$$ is odd.
II. $$30^n$$ is odd.
For the integers a, b and c with a = bc, is a > b ?
I. $$\mid a \mid = \mid b \mid$$
II. $$c^2 = 9$$
What is $$x_1 + x_2 + x_3 + x_4 + x_5 ?$$
I. $$x_3 = 20$$
II. $$x_1, x_2, x_3, x_4, x_5$$ are in arithmetic progression.
What is the average of a -3, b + 4, c - 5 and 6?
I. a, b, c are positive integers.
II. a + b + c = 100
Is $$\frac{n}{18}$$ an integer ?
I. $$6 \mid n$$
II. $$9 \mid n$$
Is $$\triangle ABC$$ scalene?
I. $$AB \neq BC$$
II. $$\angle BAC \neq \angle BCA$$
With how many zeroes does the number a = 16 ! end ?
I. $$5^3 \mid a. 5^4 \mid a$$
II. a is an even number.
Is the quadrilateral ABCD a rectangle ?
I. AB = CD, AD = BC
II. AC = BD
If P, A, B are three points on a circle, what is $$\angle APB ?$$
I. AB is the diameter of the circle.
II. The sum of the angles of $$\triangle APB$$ is $$180^\circ$$
Is the number n divisible by 2 ?
I. The sum of the digits is divisible by 2.
II. The digit in the units place is divisible by 2.
Are the roots of $$ax^2 + bx + c = 0 (a \neq 0)$$ real ?
I. 4a + b = 0
II. c = 5a
What is the area of the rectangle ABCD ?
I. E is the midpoint of AB
II. Area of the $$\triangle CDE$$ is 50 $$cm^2$$
A sequence of numbers or letters that follow a definite pattern is given. Each question has a blank space. This has to be filled by the correct answer from the four given options to complete the sequence without breaking the pattern.
3Z2A, 5X5C, 7V8E, --------
Z7A, Y6B, X5C, -------, U3E
$$\sqrt{1 + \sqrt{15}}, \sqrt{3 + \sqrt{13}}, ------------, \sqrt{10}$$
UGX : AND :: QLN : -----
---- : HDGF :: FILM : ADGH
KEGV, JDFU, ICET, --------
DIVIDEND : CHUHCDMC :: KEYBOARD : -------
13, 28, 49, 76, -----, 148
2, 26, 242, -------
$$\frac{2}{3}, \frac{8}{9}, \frac{26}{27}, \frac{80}{81}, --------, \frac{728}{729}$$
Pick the odd thing out:
Each of the questions follow a definite pattern. Observe the same and fill in the blanks with suitable answers.
0001, 0010, 0011, 0100, -------, 0110
$$\frac{1}{2}, \frac{1}{6}, \frac{2}{31}, --------, \frac{4}{391}$$
$$(x + y), (x^2 - y^2), (x + y)^2, (x - y), (x^2 - y^2)^2, (x + y)^3, (x - y)^2, --------$$
$$\frac{5}{9}, \frac{10}{28}, \frac{17}{65}, \frac{26}{126}, \frac{37}{217}, ---------$$
$$\left\{\frac{1}{5}, \frac{1}{7}, \frac{1}{9}\right\}, \left\{\frac{1}{11}, \frac{1}{14}, \frac{1}{17}\right\}, \left\{\frac{1}{19}, \frac{1}{23}, -----\right\}$$
9, 36, 100, 225, ----------, 784
W4C, T9F, Q16I, --------
$$11\frac{1}{9}, 12\frac{1}{2}, 14\frac{2}{7}, 16\frac{2}{3}, --------$$
4, 7, 12, 19, 28, 39, --------, 67
$$\frac{15}{3}, \frac{24}{5}, \frac{35}{7}, --------, \frac{63}{11}$$
A Mobile manufacturing company makes three models I, II and II of mobile phones. The production (in thousands) during the years 2009 through 2013 is given below :
If the cost of production of mobiles of I, II and III models during the year 2011 are respectively ₹ 2,250, ₹ 2,750 and ₹ 5,250 per unit, then the total cost of production (in crores of rupees) during that year is
If the profits per unit of three models I, II and III of mobiles during the year 2013 are ₹ 550, ₹ 650 and ₹ 1,000 respectively, then the total profit (in lacs of rupees) during the year 2013 is
What is the percentage increase in the production of Model II mobiles in the year 2013 when compared to the year 2010 ?
The following Pie diagram illustrates the yearly expenditure of an educational institution towards six heads : A-Staff salaries, B-Maintenance, C-Laboratories, D-Learner activities, E-Examinations and F-Miscellaneous. Using the data given answer the questions.
The total sectorial angle corresponding the heads C, D and E is
If in a year the expenditure under B is 30 lac more than the expenditure under E, then the total expenditure (in lacs) for that year is
If the annual expenditure is 200 lacs, then the expenditure towards F (in lacs) is
In a year total expenditure incurred towards E is 20 lacs of rupees. Then the expenditure towards (in lacs) is
The sectorial angle corresponding to A is
Using the data given in the below Venn diagram answer:
The number of elements in $$C - (A \cup B) =$$
The number of elements in $$A \cup (B \cap C)$$ is
The letters in the English alphabet are coded in the reverse order. For example, A is coded as Z, B is coded as Y.....
Following this code answer the questions
The code word of POCKET is
Which group of letters is coded as CODE ?
Which group of letters is coded as HAPPY ?
The code word for GROUP is
LIMIT is coded as
For the following questions answer them individually
If BOWLER ts coded as CPXMFS, then BATSMAN is coded as
If the code word for STATISTICS is UVCVKUVKEU, then the code word for COMMERCE is
If MOUSE is coded as LNTRD, then the code for COMPUTER is
If TRIANGLE is coded as RPGYLEJC the code for RHOMBUS is
If TEACHER is coded as SEABGEQ, then the code for STUDENT is
The angle between the minutes hand and hours hand when the time shown in the clock is 6.20 pm is
A big joint family has grandfather; father; mother: four sons and their wives; and two daughters of each son. How many female members are there in the family ?
As per the time table the local train leaves the station at regular intervals of 45 minutes. Reaching the station a person learnt that the train left 10 minutes ago and the next train is at 10.15 a.m. What time did the personarriveat the station ?
A car travels from A to B at a speed of 24 kmph and returns from B to A at a speed of 40 kmph. Whatis the average speed ofthe car for the whole journey (in kmph) ?
In a Queue of 51, the positions of A and aretenth and thirty fifth respectively. If C is in between A and B and equidistant from them, how manyare there (without counting C) in tront of C in the queue ?
A, B, C, D and E sit on a bench in a row such that C sits between D and E: D sits between A and C while E sits between C and B. Their seating arrangement is
If $$ab \neq 0$$ and $$a * b = \frac{1}{ab} - 1$$, then $$\sum_{k=1}^{2015}\left(\frac{1}{k^2} * k\right) =$$
If $$a ⊙ b = \sqrt{ab} + \frac{1}{\sqrt{ab}}$$ and $$a \triangle b = \sqrt{ab} - \frac{1}{\sqrt{ab}}$$, then $$\frac{4 ⊙ 9 + 4 \triangle 9}{4 ⊙ 9 - 4 \triangle 9} =$$
If today is Sunday what day of the week will it be 63 days later ?
A clock is set at 10.00 a.m. If clock loses 3 minutes every two hours, whatis the correct time whenthe clock shows 4.00 p.m. on the same day ?
In a fraction if the numerator is increased by 20% and the denominator is decreased by 20% we get new fraction $$\frac{3}{7}$$ The sum of the new fraction and the original fraction is
If 25% of a number is 25 more than 25% of 500, then the number is
By selling an item for ₹ 189, a trader gets a profit of $$12\frac{1}{2}\%$$. The cost price (in rupees) of the item is
The cost price of an item is ₹ 250. Its marked price is ₹ 360. The maximum possible discount that can be given so that a profit of 20% is made is
In a partnership, A invests $$\frac{1}{4}$$ of the capital for $$\frac{1}{4}$$ of the time; B invests $$\frac{1}{5}$$ of the capital for $$\frac{1}{2}$$ of the time while C invests the rest of the capital for the whole time. The share of A (in thousands of rupees) in the profit of ₹ 2.28 lakhs is
In a joint business, A invests ₹ 20,000 for six months while B invested certain amount for the whole year. In the year—end profit of ₹ 9,000 the share of A is ₹ 6,000. The amount(in rupees) invested by is
Pipes A, B, C canfill a tank individually in 2 hours, 3 hours and 4 hours respectively. All the three are opened for 15 minutes and pipe C is closed. The time (in minutes) required furtherto fill the tank is
Pipes A and canfill a tank in 9 minutes and 12 minutes respectively. A is opened and after sometime B is opened; and the tank is full in 4 minutes. The time difference (in minutes) between the opening of A and is
Three trains A, B and C moving at speeds $$s_1, s_2$$ and $$s_3$$ respectively take times $$t_1, t_2$$ and $$t_3$$ respectively to cover a distance of x kms. If $$t_1 : t_2 : t_3 = 20 : 15 : 12$$, then $$s_1 : s_2 : s_3 = ...........$$
The time (in seconds) taken by a train of 240 metres long travelling at 70 kmphto cross another train of length 110 metres standing on a parallel track is
10 men and 15 women can complete a work in 6 days; and 12 men and 27 women can complete the same work in 4 days. The number of days required for 2 men and 12 women to complete the same work is
A and B can doa work in 8 hours; B and C can complete the same work in 6 hours while C and A require 12 hours to complete that work. The time required by C alone to complete that work is
The area of a square S is equal to the area of the rectangle of sides 56 metres and 14 metres. The length (in metres) of diagonal of S is
The area of a rhombus is 144 square units. If one of its diagonals is 18 units then the length of the other diagonal (in units) is
A brick measures 20 cms x 10 cms x 7.5 ems. The number ofbricks required to build a wall of dimensions 25 m x 2 m x 0.75 m is
The volume ofa cone is $$108 \pi$$ cubic ems and its height is 9 cms. The base radius (in cms) ofthe cone is
A rectangular plot R of perimeter 46 metres has area 120 square metres. The area of the square whoseside is equal to the diagonal ofR, is
A wheel makes 50 revolutions in covering a distance of440 metres. The radius (in metres) ofthe wheel is
The ratio ofthe curved surfacearea to the total surface area of a right circular cylinder is 1 : 2. If its total surface area is 616 sq. cms., then the volume ofthe cylinder(in cubic ems) is
If x > 0 and $$\mid 1 - 3x \mid > 4 - x$$, then
$$(1100101)_2 - (1011011)_2$$
If $$m = 7^1. 5^2. 3^4. 2^8$$, then the greatest integer value of k such that $$21^k$$ divides m is
If $$a^x = b^y = c^z \neq 0$$ and $$b^2 = ac$$, then the progression in which x, y, z are is
Three numbers are in the ratio | : 2 : 3 and the sum of the cubes of them is 36. The smallest number among them is
The earnings of A, B, C are in the ratio 7: 9 : 12 and their expenditures arein the ratio 8:9: 15. IfA saves 25% of his earnings, then the ratio oftheir savings is
If $$x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$$ and xy = 1 then x + y =
If $$a \neq b, a^2 + b^2 \neq 0$$, then $$\frac{(a - b)\left(\sqrt{a} - \sqrt{b}\right)}{(a + b)\left(\sqrt{a} + \sqrt{b}\right)} =$$
The least positive integer m to be added to 3096 so that their sum is divisible by 39 is
If a number k is of the form 18 m + 7 for some integer m then the remainder when k is divided by 6 is
The largest number m such that the numbers 947, 639 and 1051 leave the same remainder when divided by m is
The number of pairs of positive integers a and b such that a + b = 594 and gcd (a, b) = 27 is
Taking $$\frac{1}{6.198} = 0.16134$$, the value of $$\frac{1}{0.0006198}$$ is
The rational number r that becomes $$\frac{1}{2}$$ when 1 is subtracted from the numerator and becomes $$\frac{3}{5}$$ when 1 is subtracted from the denominator is
The descending order of the fractions $$\frac{8}{13}, \frac{5}{12}, \frac{9}{11}$$ and $$\frac{7}{15}$$ is
1.57777 ..... =
$$\left(\frac{\sin 45^\circ + \cos 45^\circ + \tan 45^\circ}{\sin 45^\circ - \cos 45^\circ - \tan 45^\circ}\right)^2 =$$
$$\frac{1 - \cos \theta}{\sin \theta} + \frac{\sin \theta}{1 - \cos \theta} =$$
In $$\triangle ABC, \angle ABC = 45^\circ, \angle CAB = 30^\circ$$ and CD is perpendicular to AB. If CD = 100, then AB =
If $$7 + 10x - 5x^2$$ has maximum at $$x = \alpha \epsilon R$$, then $$\alpha =$$
The progression in which the roots of the equation $$6x^3 - 11x^2 + 6x - 1 = 0$$ lie is
The quadratic expression that leaves remainders 1, 2 and 4 respectively when divided by (x - 1), (x - 2) and (x - 3) is
If p(x) is a polynomial divisible by (x - 5), then a factor of $$p(x^3 - 3)$$ is
If $$\frac{xy}{x + y} = \frac{6}{5}$$ and $$\frac{xy}{x - y} = 6$$, then $$(x, y) =$$
The number of solutions of the system $$x - y + z = -6, x + y - z = 3, -x + y - z = 6$$ is
The sum of all the natural numbers between | and 100 which are divisible by 7 is
$$\sum_{k=0}^{\infty}\frac{2^k}{3^{k+1}} =$$
If the fourth term in the binomial expansion of $$\left(2^x. x^2 + \frac{1}{x^2}\right)^6$$ is 160, then x =
The middle term in the expansion of $$\left(x^2 - \frac{1}{x}\right)^8$$ is
$$A = \begin{bmatrix}1 & 2 & 2 \\2 & 1 & 2 \\2 & 2 & 1 \end{bmatrix} \Rightarrow A^2 - 4A =$$
If det A = 5 for a $$3 \times 3$$ matrix A, then det(5A) =
$$\lim_{x \rightarrow 3}\frac{x - 3}{\sqrt{x - 2} - \sqrt{4 - x}} =$$
$$\lim_{x \rightarrow \frac{\pi}{2}}\frac{1 - \sin^3 x}{\cos^2 x} =$$
In $$\triangle ABC, \angle BAC = 90^\circ, AD \perp BC, AD = 6$$ cm and BD = 4 cm. Then DC =
The vertices A, B, C, D in that order of a quadrilateral lie on a circle. Then $$\angle ABC + \angle ADC =$$
If a square is inscribed in a circle of radius $$\sqrt{\frac{2015}{2}}$$ then area of the square is
For $$\triangle ABC$$ with vertices A(4, 2), B(6, 5) and C(1, 4) the length of the median through A is
If A (k, -3), B (2, -5) and C (-1, -8) lie on a line, then AB : BC =
For statements p and q, the tautology among the following is
If p and q are statements, then the inverse of $$p \rightarrow q$$ is
If $$I_k = \left\{x \epsilon R: 0 < x < \frac{1}{k}\right\}$$ for k = 1, 2, 3, ....... then $$\bigcap_{k=1}^{\infty}I_k = $$
For sets A, B and C, $$A - (B \cup C) =$$
If $$f: R \rightarrow R$$ and $$g : R \rightarrow R$$ are defined by $$f(x) = 2^x$$ and $$g(x) = x^2$$ for each $$x \epsilon R$$, then
$$\left\{x \epsilon R : (fog)(x) = (gof)(x)\right\} =$$
The length of the line segment intercepted between the axes by the line joining (6, -4) and (-3, 8) is
The angle between the lines 2x + 3y = 5 and 2(x - 1) + 3(2 + y) = 6 is
$$\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ} =$$
For $$n \geq 1$$, let $$a_n = k$$ where k is the remainder when n is divided by 5. Then the mode of the observations $$a_1, a_3, a_8, a_{12}, a_{13}, a_{17}, a_{23}$$ is
The standard deviation of 1, 2, 3, ...., 25 is
If $$\sigma^2$$ is the variance of $$x_1, x_2, ........, x_n$$ then $$9 \sigma^2$$ is the variance of
The correlation coefficient r satisfies the inequality
A ball is drawn at random from a bag containing 5 green, 6 black and 7 white balls, all of identical size. The probability that the chosen ball is either green or black is
Three numbers are chosen at random fromthe set {1, 2, 3, ..., 8}. The probability that they are consecutive numbers is
The probability that a number chosen at random from {1, 2, 3, 4, .... 14} is a prime number solution of the equation f(x) = 0 where $$f(x) = (x - 2) (x^2 - 9) (x - 6) (x - 8)$$ is
If A and B are events such that $$P(A) = \alpha, P(B) = \beta$$ and $$P(A \cap B) = \gamma$$, then $$P(\overline{A} \cup B) =$$
The arithmetic mean of the distribution given below is
The median of the first sixteen even natural numbers is
Choose the correct meaning of the word given :
Caveat
Conundrum
Indubitably
Expedient
Proscribe
Timbre
Fill in the blank choosing the correct word :
The beauty of the flowers at the Mughal Garden in Delhileft the visitors ---------
The bus suddenly ------------ to avoid an accident with a speeding motorist.
The -------- climate helped him regain his health.
Dueto the unseasonalrains, agricultural produce for the current year remained ----------
Choose the correct answer:
A special text file that a web server places on a visitor’s computer is called
‘MICR’ stands for
A system configuration in which two or more computers in a network share applications, storage and processing power is called
A summary of the aims and values of an organization is called
A type of decision making which generally involves a group of high-level managers who deal with very complex, largely unstructured and non-routine problems which affect the general direction ofthe organization is called
A marketing strategy that includes high price and high promotional cost while launching a new product is called
Who, amongthe following, is deemed to be the founder of Scientific Management ?
M.B.O. stands for
One of the most common network setups where each of the devices and computers on a network connect to a central hubis called
A non-volatile computer storage that can be electrically erased and reprogrammed is called
A: “Why doesn’t she see through him ?”
B: “Why, what do you expect to happen ?”
In this conversation, ‘B’ is
A: “Why don’t you cook the dinner today ?”
B: “I wish you'd let me be.”
‘B’ implies
A: “Theyare talking ill of me, although they are not ignorant 6f my merit and hard work.”
B: “Be it so, dogs bark while the caravan passes on.”
‘B’ means that
Changethe following into passive voice :
All desire wealth and some acquireit.
A: “Why don’t you save some money from your salary every month ? It will help you in the long run.”
B: “It’s rather hard in the circumstances. I can barely make ends meet.”
'B’ implies that his salary is
He cleared out without paying the rent.
The underlined phrase means
A: “Can you buy souvenirs at the market ?”
B: “You can, but you may be cheated.”
‘B’ implies
Fill in the blanks with the appropriate phrase/verb/preposition :
He pushed his way ----------- the crowd.
The sea has --------- all round the coast.
He was ---------- with immense physical strength
To ---------- criminal behaviour is to encourage social ills.
Please ------- the proposal and let me know what you think.
I find it very hard to ---------- his lectures.
Cut a piece --------- the bread.
The level of inflation has increased ---------- 40%
Read the following passage and answer questions:
Passage:
Computers have brought a revolution in human life. To begin with, computers took over different human activities. Now even thinking and problem-solving are being done by computers. This has culminated into automation of offices and manufacturing processes resulting in drastic reduction of manpower in administration, business and industry. So much is the human reliance on computers that they are being used on a large scale even in fields like music, sculpture and architecture. The growing use of computers in teaching might one day render teachers, classrooms andlibraries redundant. This situation makes many of us believe that computers are likely to replace human beings in every walkof life. But every coin has two sides. However useful they may be, computers cannot replace human beings. A compliment by an elderly person restores the confidence of a depressed person. A simple touch of a mother silences a crying baby. Can a computer perform these and many such other miracles ? Now-a-days, teaching is being done by computers. Computer lovers claim that they can learn everything with the help of a computer. But imagine the difference between the two situations, i.e.: sitting before a computerandsitting in a classroom with dozens of students around and in the presence of a teachers. The pains and pleasures of companionship, the repudiating as well as encouraging expressions on the teacher’s face, the direct interaction, and abundant sharing and understanding,set this living situation a world apart from the lonely, computer controlled suffocating room.
What is the meaning of ‘automation of offices and manufacturing processes’ ?
What makes one believe that computers will one day replace human beings ?
Why cannot computers replace humanbeings ?
What does a ‘lonely, computer-controlled suffocating room’ imply ?
How have computers brought about a revolution in human life ?
Read the following passage and answer questions
Passage:
How many times have you asked, “Why did he do that ? Why did she say that ? Why does nothing ever work out for me ? Why didn’t I get what I wanted ? Why does this keep happening in my life ?” “Whyology” is the obsessive need to know why things happen as they do, which results in emotional paralysis, keeping you stuck. Why do you need to know why things happen ? If you did know, would it make that much difference ? Many people will say, “Yes, it would make a difference, because then I would be able to move on and let go.” The truth is that the letting-go experience has nothing to do with knowing why things happen as they do. In fact the more you need to know why,the less likely you are to let go and more on. Unless you release this cycle, you will be robbed of your ability to appreciate and enjoy the moment you are living in right now. Think of all the energy that you could use to create in life if you left the practice of keeping vigil on tombstones. Internal stress comes when you resist what is in life. When you release your need to know why, an amazing thing starts to happen. You begin to connect with your inner creativity, which helps you find creative solutions to your situation.
What does ‘Whyology’ lead to ?
What happens when this cycle of ‘whyology’ is released ?
What does the ‘practice of keeping vigil to tombstones’ mean ?
When does ‘internal stress’ occur ?
What is ‘Whyology’ ?
Read the following passage and answer questions:
Passage:
Tea has always been an integral part of our beverage culture. Its origins are the stuff of legend. A Chinese story says that when an Emperorwaspurifying waterin the shelter of a tea tree, some leaves fell into the pot. The liquid that emerged after boiling was of a wonderful fragrance, colour and taste, and the first tea to be brewed. In India, we are told of a Prince, who left his homeland to preach Buddhism and decided notto sleep duringhis. nine-year mission. At the end of his third year, overtaken by exhaustion, he chewed a few leaves of a tea shrub, which apparently enabled him to stay awake for the remaining six years. Over the years, tea drinking was refined into an art and indeed has even been elevated into an elaborate, almost sacred rite as in the Japanese tea ceremony. But if there was one culture that adopted tea drinking and madeit an iconic ritual and time of day in itself, it was the English.
According to legend, how werethefirst tea leaves discovered ?
What did tea drinking gradually become a form of?
Who first related tea drinking to “the time of day” ?
Which of the following is not mentioned in the passage ?
What does the origin oftea drinking suggest ?
